i need help with solving the above problem

i need help with solving the above problem

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Hi Kristen,

Using the rule of exponents:

(x^{m})^{n} = x^{m * n}

so, (f ^{-3})^{-1} = f ^{(}^{-}^{3} * ^{
-1) }= f ^{3 }and so, the expression becomes:

f^{ -5}/ (f ^{-3})^{-1}= f ^{-5} / f ^{3}

The rule of exponents x^{m} / x^{n} = x^{m-n} tells us that we can re-write the expression as:

f^{ -5 - (3)} = f ^{-8} or

1/ f ^{8}

since a negative exponent tells us that the term is below the division bar or the denominator of a fraction.

Hope this helps!

Kristen.... think of a negative exponent as a halo on a variable or number...if the halo is positive, then it is on the proper side of the division bar....if the halo is negative, then it is out-of-place....move it to the other side of the division bar...in your question above the top variable "f" has a (-5) exponent...so move it out of the numerator into the denominator and change the (-5) to a (+5)...its in the "proper place"...as for the f^-3 to the -1...use rule of exponents and it simplifies to f^3 ( -3 times -1 = +3). Hence, we have eight f's in the denominator and a one in the numerator .... ANSWER is 1/f^8

less wordy way to solve....use rules of exponents X^m/X^n = X^(m-n)....f^-5-(3) = f^-8 = 1/f^8